For the digital evaluation of the measurement results of sensors, it is necessary to convert the analog sensor signal, or the signal sampled by sensors, into a digital signal. Frequently, for this purpose analog-digital converters are used, which make use of the advantages of an oversampling. Here, the narrow-band input signal is sampled with a high-frequency clock rate, and is subsequently digitized using an analog-digital converter. The bandwidth of the useful signal (also referred to as useful band or base band) is here significantly smaller than half the sampling frequency. If the input signal contains high-frequency interference signals, these may be convoluted down into the useful band due to the aliasing effect. In order to prevent this, standardly an anti-aliasing filter is used that filters out the high-frequency interference signals before the sampling.
FIG. 1 schematically shows a frequency diagram for such a situation. Analog useful signal 16 is sampled with a sampling frequency f. In an idealized circuit, or an idealized method, this takes place for example using a periodic clock signal having the period T=1/f, a sampled value being acquired in each case at a determined point in time within the period, for example when the periodic clock signal exceeds or falls below a specified voltage, so that the temporal distance between two successive sampling times corresponds in each case to the period T. The sampled useful signal then results, in the time representation, as the product of the input signal times a sampling function that is given by a sequence of equidistant sampling pulses with the temporal spacing T. In the frequency representation, this product corresponds to a convolution of the frequency spectrum of the input signal with the frequency spectrum of the sampling function, given by a sequence of equidistant spectral lines with the spacing f. Frequency spectrum 10 of a sampling function is shown in FIG. 1.
The input signal can contain superposed high-frequency interference signals, such as those that occur for example in the case of electromagnetic coupling in. According to the existing art, such an interference signal is filtered out before the sampling using an anti-alias filter, for example a low-pass filter having transmission function 14. Such a filtered high-frequency interference signal 12 is shown in FIG. 1 as an example, at a frequency that is slightly greater than twice the sampling frequency f. The point of intersection of transmission function 14 of the anti-aliasing filter with the frequency axis limits base band 1 to a range that extends from 0*f up to a frequency of f/2. Here, the low-pass filter is fashioned such that an analog useful signal 16 in base band 1 is allowed to pass through as unfiltered as possible at a typical useful frequency. A disadvantage of this solution is that an anti-aliasing filter has to be implemented. This results in development outlay and use of surface area, in particular if an application-specific integrated circuit (ASIC) is realized.
FIG. 2 shows the frequency spectra of the sampling of an analog useful signal 16 without anti-aliasing filter. Base band 1 extends, as in the case of the filtering using an anti-aliasing filter, over a frequency range of from 0*f to f/2. However, interference amplitude 20, which represents the convolution of an unfiltered high-frequency interference signal 18 in the case of sampling without the use of the anti-aliasing filter, is for the most part convoluted directly into base band 1 and thus, given sampling with a sampling frequency f whose frequency spectrum 10 in FIG. 2 is depicted as equal to that in FIG. 1, is wrongly interpreted as useful signal 16.
In the article “Digital Alias-free signal processing in the GHz frequency Range” by I. Bilinksis, G. Cain, published in 1996, pages 6/1-6/6 (XP1133893), the authors discuss a sampling method freed from aliasing, in which the sampling times are shifted in time by an arbitrary amount of time with respect to a periodic sampling.
Furthermore, U.S. Pat. No. 5,485,273 discusses a resolution system reinforced by a ring laser gyroscope, in which a phase-locked loop circuit used for sampling frequency modulation is used in combination with a fast filter.
Moreover, EP 1 330 036 A1 discusses a method and a device for alias-suppressed digitization of analog signals of a high frequency, in which a clock pulse generator generates a sequence of electrical pulses of a predetermined frequency Fclk, the sequence being divided by a pseudo-arbitrary value for the purpose of selecting a pulse from the sequence.